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J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 2, Pages 265–272 (Mi jsfu184)  

Conditions for convexity of the isotropic function of the second-rank tensor

Vladimir M. Sadovskii

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia

Abstract: For a scalar function, depending on the invariants of the second-rank tensor, condition of convexity and strong convexity are obtained with respect to the components of this tensor in an arbitrary Cartesian coordinate system. It is shown that if a function depends only on the four invariants: three principal values of the symmetric part of a tensor and modulus of pseudovector of the antisymmetric part, these conditions are necessary and sufficient. A special system of convex invariants is suggested to construct potentials for the stresses and strains in the mechanics of structurally inhomogeneous elastic media, exhibiting moment properties.

Keywords: isotropic tensor function, convexity, invariants, nonlinear elasticity, plasticity.

Full text: PDF file (155 kB)
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UDC: 517.17+539.37
Received: 18.09.2010
Received in revised form: 25.10.2010
Accepted: 10.12.2010

Citation: Vladimir M. Sadovskii, “Conditions for convexity of the isotropic function of the second-rank tensor”, J. Sib. Fed. Univ. Math. Phys., 4:2 (2011), 265–272

Citation in format AMSBIB
\Bibitem{Sad11}
\by Vladimir~M.~Sadovskii
\paper Conditions for convexity of the isotropic function of the second-rank tensor
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2011
\vol 4
\issue 2
\pages 265--272
\mathnet{http://mi.mathnet.ru/jsfu184}


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